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प्रश्न
The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given that the number triples in 5 hours, find how many bacteria will be present after 10 hours?
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उत्तर
Let x denote the number of bacteria at time t hours.
Given = `("d"x)/"dt"` = kx
Hence `("d"x)/x` = kdt
∴ x = C ekt
Suppose x = x0 at time t = 0
x0 = C ek(0)
= C e° = C
∴ C = x0
Hence x = x0 ekt
At time 5, x = 3x0
∵ Number triple in 5 hrs
∴ Hence 3x0 = x0 e5k
∴ e5k = 3
when t = 10,
x = x0 e10k
= x0 (e5k)2
= x0 32
= 9x0
∴ After 10 hours, the number of bacteria as 9 times the original number of bacteria.
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